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Kth Largest Element in an Array – Solution & Complexity

Interview solutions
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Kth Largest Element in an Array

Solution Walkthrough

  1. Step 1: Understand the Goal

    • Identify the required output and the state that changes.
    • Use the examples to rule out tempting but incorrect interpretations.

  2. Step 2: Choose the Core Pattern

    • This problem is best exposed by Maintain a min-heap containing only the k largest values.
    • Maintain only the state needed for the next operation.

  3. Step 3: Build the Algorithm

    • Process each state once when possible.
    • Record state before scheduling dependent work to avoid duplicates.

  4. Step 4: Check Edge Cases

    • Verify the smallest input, impossible cases, and repeated values where allowed.
    • Keep output ordering deterministic.

  5. Step 5: Final Solution and Complexity

    • Time complexity is O(n log k).
    • Space complexity is O(k).
    def find_kth_largest(nums: list[int], k: int) -> int:
    import heapq
    heap = []
    for number in nums:
        heapq.heappush(heap, number)
        if len(heap) > k: heapq.heappop(heap)
    return heap[0]

FAQ

See also

Practice Kth Largest Element in an Array online (run code in the browser)K Closest Points to Origin solution (medium)Top K Frequent Elements solution (medium)Find Median from Data Stream solution (hard)Merge K Sorted Lists solution (hard)All coding interview problems
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